A number of technologies, such as quantum communication, quantum calculation, etc., rely on a source of photon pairs (e.g., an entangled photon pair comprising an idler photon, ωi, and a signal photon, ωs) which can facilitate confirmation that a received photon pair is valid. Conventional approaches to providing the photon pairs include parametric down conversion (PDC) which can utilize bulk optics, and also four-wave mixing (FWM) which can utilize fiber optics. A detriment of PDC is that the direction of the photon pair is completely random, hence a pair of photons can be symmetrically opposite but no prediction can be made with regard to the photon direction in either of the positive direction of a first photon or a negative direction of a second photon. Accordingly, large bulk optic lenses are utilized to facilitate capturing as many photons as possible across the range of potential directions, while the collected number of photons is limited by the acceptance angle of the device receiving the photons.
The problem of photon directionality can be addressed by FWM in a waveguide based system, but owing to such effects as Raman scattering, a conventional approach of generating ωi and ωs based upon a pulse comprising a pair of pumped photons ωp1 and ωp2 can lead to uncertainty regarding whether the ωi and ωs photons have been formed and received as expected.
For instance, with reference to FIGS. 7 and 8, an idler photon ωi, in idler pulse 730, and a signal photon ωs, in signal pulse 740, are generated by a pair of pump photons ωp1 and ωp2, in pump pulses 710 and 720, where for degenerate FWM, ωp1 and ωp2 can have a common frequency, ωp. As shown in FIG. 7, the frequency of the respective pulses are ωiωpωs. In an aspect, the photon pairs can be generated at frequencies ωi and ωs by inserting a strong field at the pump frequencies ωp, hence ωp acts doubly as ωp1 and ωp2. Each pair of pump photons, ωp1 and ωp2, are effectively destroyed in a pump pulse during the energy exchange occurring between the destroyed pump photons ωp1 and ωp2, and the newly created ωi and ωs. Accordingly, per a spontaneous FWM process, the pumped pair ωp1 and ωp2 disappear and the idler/signal pair ωi and ωs arise, or the idler/signal pair ωi and ωs disappear and the pumped pair ωp1 and ωp2 arise.
A rate of generation of a photon pair ωi and ωs, rate r1, can be determined in accordance with Equation 1:
                              r          1                ∝                              γ            2                    ⁢                      P                          p              ⁢                                                          ⁢              1                                ⁢                      P                          p              ⁢                                                          ⁢              2                                ⁢                      ∫                          ∫                                                sinc                  ⁡                                      (                                                                  Δ                        ⁢                                                                                                  ⁢                        kL                                            2                                        )                                                  ⁢                                  exp                  ⁡                                      [                                          -                                                                                                    (                                                                                          Δω                                                                  p                                  ⁢                                                                                                                                          ⁢                                  1                                                                                            +                                                              Δω                                                                  p                                  ⁢                                                                                                                                          ⁢                                  2                                                                                                                      )                                                    2                                                                          2                          ⁢                                                      σ                            2                                                                                                                ]                                                  ⁢                                  ⅆ                                      ω                                          p                      ⁢                                                                                          ⁢                      1                                                                      ⁢                                  ⅆ                                      ω                                          p                      ⁢                                                                                          ⁢                      2                                                                                                                              Eqn        .                                  ⁢        1            
where γ=nonlinearity coefficient of a fiber, Pp1=pump power at ωp1, Pp2=pump power at ωp2, k=phase propagation constant, L=fiber length, ωi=idler photon wavelength, ωp1,2=pump photon frequencies, σ=spectral bandwidth of pump pulses.
Further, for a high efficiency of operation in generating photons at ωi and ωs there is a requirement for two conditions to be satisfied: (a) energy conservation and (b) momentum of conservation (also referred to as phase matching). Energy conservation indicates that a photon pair will always exist, hence, if two existing photons are destroyed at the pump then two new photons will be formed, one idler photon in the idler pulse and one signal photon in the signal pulse, per Equation 2:ωs+ωi−2ωp=0  Eqn. 2
The momentum of conservation is satisfied per Equation 3:ks+ki−2kp−2γPp=0  Eqn. 3
where ks, ki, and kp are the respective propagation constants for the respective ωi, ωs, and ωp1 & ωp2, for a forward mixing gain, while the fiber nonlinearity γ in conjunction with the pump power P can provide a measure of the effect of the fiber nonlinearity for a given pump power.
Theoretically, the total photon distribution between ωp1 & ωp2 and ωi& ωs should be preserved. Unfortunately, various deleterious effects can affect generation and/or propagation of the various photons, such an effect being Raman scattering which can scatter photons into different wavelengths, e.g., by a non-linear mechanism. FIG. 8 presents a Raman scattering effect and an associated frequency and bandwidth offsets for photons generated by an oscillator. The Raman gain shape 810 is presented along with theoretical gain shapes 820 (for the ωi photon) and 830 (for the ωs photon), each gain shape has been normalized individually. In an aspect, the idler photon and signal photon frequencies are determined by the propagation constants and the nonlinearity of the waveguide, per Eqn. 3. It is to be noted that the Raman scattering only occurs on the idler side of the frequency range in optical fibers, with a peak generation of about −13 THz, which is the resonant frequency between molecular heat and molecular vibration of a waveguide molecular lattice. In other words, fiber material only dissipates energy from the optical waves to the heat bath (converting high energy, high frequency photons to lower energy, lower frequency, photons), instead of adding energy to the optical wave. Which process dominates depends on material characteristics.
In a waveguide (e.g., a fiber) carrying a ωi photon, Raman scattering 810 can add an uncorrelated photon at ωi, which confuses the photon number entanglement between ωi and ωs. Ideally, a transference of energy between the light field (e.g., the ωp photon) and the waveguide molecules is a lossless operation. However, owing to each waveguide molecule being connected to adjacent molecules, some of the transferred energy can be lost as heat radiation dissipating throughout the waveguide structure as the molecular lattice vibrates under the stimulation of the impinging ωp photon. The loss of energy to the molecular lattice leads to the overall energy no longer being available to form a photon(s) of the same optical equivalent (e.g., wavelength, frequency, etc.) as that of the impinging ωp photon; any new photon which is formed in the waveguide will re-enter the light field but with an energy smaller than that of the impinging ωi photon. This Raman process is separate from the desired four-wave mixing process. The consequence of the addition of a photon on the idler frequency via the Raman process is that the number of photons between the idler and that of the signal may differ. To facilitate measurement of the ωi photon(s) and the ωs photon(s), the respective photons can be split and directed to two separate optical waveguide paths, e.g., an idler leg and a signal leg. A count can be taken on each of the legs to determine the number of ωi photon(s) vs. the number of ωs photon(s), with, theoretically, the entangled photons generating the same number of photons on both legs. However, per the above, the number of ωi photons on the idler leg can be greater than the number of ωs photons on the signal leg. The correlation of photons on each leg of a conventional system is no longer 100% pure owing to the Raman scattering contamination.
As shown in FIG. 9, as the rate of generation of the various photons is increased, so the number of unwanted photons being generated as a function of Raman scattering is also increased. Plot 910 indicates an increase in the rate of entangled photon generation (count per second, cps) as the pump input power is increased from about 0.2 mW to about 1.0 mW. However, as the pump input power is increased there is a corresponding increase in the number of unwanted photons formed, per plot 920, where plot 920 is a plot of pump input power vs. coincidence/accident ratio (plotted in log scale). Coincidence indicates that the number of photons on the idler leg and the signal leg are equal, e.g., for each idler photon there is a corresponding signal photon. Accident indicates the number of photons which are different between the idler leg and signal leg, e.g., there may be X idler photons vs. Y signal photons where X>Y. At about 0.2 mW, plot 920 indicates a coincidence/accident ratio of between about 1 in 1000 and about 1 in 10,000. At about 1 mW, plot 920 indicates the coincidence/accident ratio has reduced to about 1 in 10, a high degree of Raman scattering contamination is occurring. Hence, while increasing the pump input power (per Eqn. 1, where r1 is squarely proportional to the pump power Pp2) increases the rate at which the entangled photons are formed, the increased pump input power also results in an increase in the number of unwanted electrons formed. Furthermore, as shown in FIG. 8, the Raman spectrum has such a broad spectrum that it can be difficult to avoid when using a conventional FWM degenerate pumping approach.
Hence, for a system operating based upon detection of a co-formed photon pairing comprising of a ωi and ωs, the effects of (a) the shifting of the ωi photon, and/or (b) generation of further ωi photons from an originating ωi photon can lead to an erroneous determination that a received pair of photons ωi and ωs are actually correlated (e.g., are the original entangled pair). While the FWM mechanism is elastic in terms of energy conservation, Raman scattering fails to conserve the energy leading to breakage of the photon entanglement which can be detrimental to many quantum-based operations. For example, numerous quantum information science applications requires true single-photon source. Having a perfect correlation between the number of photons at the idler and the signal frequencies, one can gate the output of the signal frequency while counting the photons at the idler frequency. Only when the counted number of photons at the idler frequency is one, the gate at the signal frequency opens letting the signal photon out. This is one way of realizing a true single photon source using a perfectly entangled photon pair source. Especially quantum communication strictly requires only one photon at a time. Otherwise, an eavesdropper can tap the extra photon and obtain the information while being unnoticed.